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In addition to the striking beauty inherent in their complex nature, fractals have become a fundamental ingredient of nonlinear dynamics and chaos theory since they were defined in the 1970s. Moreover, fractals have been detected in nature and in most fields of science, with even a certain influence in the arts. Fractal structures appear naturally in… (More)

- Francisco J. Escribano, Luis López, Miguel A. F. Sanjuán
- IEEE Trans. on Circuits and Systems
- 2008

- Gouhei Tanaka, Borja Ibarz, Miguel A F Sanjuan, Kazuyuki Aihara
- Chaos
- 2006

The present paper studies regular and complex spatiotemporal behaviors in networks of coupled map-based bursting oscillators. In-phase and antiphase synchronization of bursts are studied, explaining their underlying mechanisms in order to determine how network parameters separate them. Conditions for emergent bursting in the coupled system are derived from… (More)

- J P Baltanás, L López, +4 authors M A F Sanjuán
- Physical review. E, Statistical, nonlinear, and…
- 2003

We consider an overdamped bistable oscillator subject to the action of a biharmonic force with very different frequencies, and study the response of the system when the parameters of the high-frequency force are varied. A resonantlike behavior is obtained when the amplitude or the frequency of this force is modified in an experiment performed by means of an… (More)

- Borja Ibarz, Hongjun Cao, Miguel A F Sanjuán
- Physical review. E, Statistical, nonlinear, and…
- 2008

A system consisting of two map-based neurons coupled through reciprocal excitatory or inhibitory chemical synapses is discussed. After a brief explanation of the basic mechanism behind generation and synchronization of bursts, parameter space is explored to determine less obvious but biologically meaningful regimes and effects. Among them, we show how… (More)

- Borja Ibarz, José Manuel Casado, Miguel A F Sanjuán
- Physical review. E, Statistical, nonlinear, and…
- 2007

We study the dynamics of networks of inhibitory map-based bursting neurons. Linear analysis allows us to understand how the patterns of bursting are determined by network topology and how they depend on the strength of synaptic connections, when inhibition is balanced. Two kinds of patterns are found depending on the symmetry of the network: slow cyclic… (More)

- Borja Ibarz, Gouhei Tanaka, Miguel A F Sanjuán, Kazuyuki Aihara
- Physical review. E, Statistical, nonlinear, and…
- 2007

Through phase plane analysis of a class of two-dimensional spiking and bursting neuron models, covering some of the most popular map-based neuron models, we show that there exists a trade-off between the sensitivity of the neuron to steady external stimulation and its resonance properties, and how this trade-off may be tuned by the neutral or asymptotic… (More)

- Jesús M Seoane, Jacobo Aguirre, Miguel A F Sanjuán, Ying-Cheng Lai
- Chaos
- 2006

Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that… (More)

- Jesús M Seoane, Miguel A F Sanjuán, Ying-Cheng Lai
- Physical review. E, Statistical, nonlinear, and…
- 2007

The effect of weak dissipation on chaotic scattering is relevant to situations of physical interest. We investigate how the fractal dimension of the set of singularities in a scattering function varies as the system becomes progressively more dissipative. A crossover phenomenon is uncovered where the dimension decreases relatively more rapidly as a… (More)

- Luis López, Miguel A F Sanjuán
- Physical review. E, Statistical, nonlinear, and…
- 2002

In the context of complex network systems, we model social networks with the property that there is certain degradation of the information flowing through the network. We analyze different kinds of networks, from regular lattices to random graphs. We define an average coordination degree for the network, which can be associated with a certain notion of… (More)